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Attractive, strange behaviour
The way to unlocking the hidden structure of a chaotic system is in determining its preferred set of behaviors - known to mathematicians as its attractor. We may not be able to predict precisely how a chaotic system will behave, but knowing the attractor allows us to narrow down the possibilities.
The attractor can be illustrated by putting a ping-pong ball into the ocean. If released above the water, it will fall - if released underwater, it will float. No matter where it starts, the ball will immediately move in a predictable way towards its attractor - the ocean surface.
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Possible behaviours of a system
A "phase space" is used to describe the possible behaviors of a system geometrically. Phase space is not always like regular space: each location in phase space correlates with a different system configuration.
In phase space, a stable system will move predictably towards ...
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Understanding the butterfly effect
A good way to see the butterfly effect is with a game of billiards. No matter how consistent you are with the first shot, the smallest of differences in the speed and angle with which you strike the white ball will cause the balls to scatter in different directions every time.
What at ...
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Phase space application
Phase space has an important application in understanding your heartbeat.
- The millions of cells that make up your heart are continually contracting and relaxing separately as part of an intricate chaotic system with complicated attractors.
- The millions of cells must work in ...
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Collisions with Earth
The solar system is a chaotic system too. The effect of chaos cannot be ignored. Keeping an eye on asteroids and other bodies is worthwhile, since chaotic forces may one day fling an unwelcome surprise in the direction of the earth.
Feeding those predictions into our equations can...
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Tiny variations vastly affect the outcome
Order on a small scale can produce chaos on a larger scale. In systems that behave without chaotic effects, small differences could eventually increase in size until they produce large effects - the hallmark of a chaotic system.
Meteorologist Edward Lorenz made this profou...
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Chaos Theory
Chaos Theory is a mathematical toolkit that allows us to extract ordered structures from chaos. The theory can reveal the intricate workings of such diverse natural systems as the beating of the human heart and the trajectories of asteroids.
At the center of Chaos Theory is the fas...
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